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Measurement back-action imposes a fundamental limit on the precision of interferometric measurements of mechanical motion, setting the standard quantum limit (SQL) for continuous opto-mechanical detection. Back-action evading (BAE) measurement schemes provide a route to surpass this limit by selectively measuring a single quadrature of motion, rejecting all back-action noise onto the other one. Practical implementations are often limited by tuning capabilities and ultimately intrinsic instabilities.
It has been theoretically shown that two-tone driving schemes enables one to perform BAE measurements [1]. Further experiments demonstrated the effect using microwave opto-mechnanics at low temperatures [2]. A recent work has addressed the issue of the two-tone instability, studying the dynamic range accessible to BAE optomechanical
measurements [3]. This work was both experimental and theoretical, but the agreement between the two, even phenomenologically correct, shows discrepancies. Here we demonstrate very good agreement between theory and microwave opto-mechanics experiments, starting from a complete Hamiltonian that incorporates all instrumental imperfections. We observe the effect of mistunings on the system in all possible parameters, including the power imbalance of the pumps which was not addressed before. We also study the physical limit of tuning for BAE measurements, showing that this limitation is a resultant of the intrinsic noise inside the system.
[1] A A Clerk, F Marquardt, and K Jacobs. Back-action evasion and squeezing of a mechanical resonator using a cavity detector. New Journal of Physics, 10(9):095010, Sep 2008.
[2] J. B. Hertzberg, T. Rocheleau, T. Ndukum, M. Savva, A. A. Clerk, and K. C. Schwab. Back-action-evading measurements of nanomechanical motion. Nature Physics, 6(3):213–217, Dec 2009.
[3] Itay Shomroni, Amir Youssefi, Nick Sauerwein, Liu Qiu, Paul Seidler, Daniel Malz, Andreas Nunnenkamp, and Tobias J. Kippenberg. Two-tone optomechanical instability and its fundamental implications for backaction-evading measurements. Physical Review X, 9(4), Oct 2019.